Chapter 11, Problem 9CR

To determine

Simplify the expression: $\frac{4-c}{2c-8}$ and state any excluded values.

Answer to Problem 9CR

  $\frac{4-c}{2c-8}=-\frac{1}{2}$ ; Excluded value: $c\ne 4$

Explanation of Solution

Given: Simplify the expression: $\frac{4-c}{2c-8}$

Concept Used:

Rational expression is in the form $\frac{\text{P}}{\text{Q}}$ , where $\text{Q}\ne 0$ , denominator cannot be zero in any rational expression.

Excluded values are also called points of discontinuity. These are the values that make the denominator equal to zero and are not part of the domain.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify.

Calculation:

In any rational function, the denominator cannot be zero.

  $\frac{4-c}{2c-8}=\frac{-1(c-4)}{2(c-4)}=-\frac{1}{2}·\frac{c-4}{c-4}=-\frac{1}{2}[\text{Rule}:b-a=-1(a-b)]$; Excluded value: $c\ne 4$

Thus, $\frac{4-c}{2c-8}=-\frac{1}{2}$ ; Excluded value: $c\ne 4$